The population of chipmunks at a nature preserve is modelled…

The population of chipmunks at a nature preserve is modelled by the function \(P(t)=\dfrac{`a`0}{1+7e^{-0.035t}}+`b`0\) adult chipmunks, where \(t\) measures the time, in months, since chipmunk monitoring began at the site. What does this model predict for the maximum number of chipmunks at the preserve?   Desmos (click to reveal)

The metabolism of a \(t\)-day-old albatross chick is given b…

The metabolism of a \(t\)-day-old albatross chick is given by \(m(t)\) watts per kilogram (\(\tfrac{W}{kg}\)).  \(m\,^\prime(10)=2\) means that when an albatross chick is old, its metabolism is . \(m(10)=4\) means that when an albatross chick is old, its metabolism is .    

Suppose \(f(x)=\dfrac{10\ln(x)}{\sqrt{x}}.\) To numerically…

Suppose \(f(x)=\dfrac{10\ln(x)}{\sqrt{x}}.\) To numerically estimate the value of \(f\,’\,(2)\), accurate to one decimal place, fill out the tables below. Be sure to round to the exact number of decimal places required!  Desmos (click to reveal)   \(b\to 2^-\) average rate of change 1.9   \(b\to 2^+\) average rate of change 2.1 From our tables we conclude that \(f\,’\,(2)=\) .